3. EXTRASOLAR PLANETS

The solar system was not the only place to provide for planetary
drama. During the past eight years we have witnessed the number of known
extrasolar planets orbiting Sun-like stars going from zero to
about one hundred at the time of this writing! The human fascination
with the possibility of discovering extraterrestrial life has helped
turn planet detection into one of the major frontiers of today's
astronomy.

The Hubble Space Telescope's contributions to this exciting field have
been related mostly to the discovery of circumstellar disks from which
planets form, and these will be described in
Section IV. In two
cases, however, HST has produced three truly unique sets of
observations, one in a globular star cluster, and two following the
light curve and spectrum of a transiting planet.

The discovery of a planet orbiting the star 51 Peg
(Mayor and
Queloz 1995)
in a remarkably tight orbit of 4.231 days challenged prevailing
theoretical views and marked the start of a "Golden Age" in planet
discoveries by radial velocity surveys (see, for example,
Marcy et al. 2000).
The existence of gas giant planets in very close orbits (at
0.04-0.05 AU) enables even photometric searches for these
planets ("hot Jupiters"). At such small separations, the probability of
the planet transiting ("eclipsing") the parent star, given random
orbital inclinations, is about 10%. More precisely, from Kepler's laws,
the duration of a transit in hours (reduced by
/ 4 for average chord length)
is given by

(4)

where M*, R* are
the stellar mass and radius in solar units and
Porb is the orbital period in days. The
probability of a transit per system is given by

(5)

Transits are very important because of the following reasons:
(a) With transits one can immediately obtain the size of
the planet [the transit depth is equal to (Rp /
R*)2]. (b) In the case of
transits, measurements of radial velocities immediately provide the
planet's mass (and not just
mpsin i, where i is the otherwise
unknown orbital inclination). (c) A knowledge of the mass and
radius can be used to test theoretical
mass-radius relations for close-orbiting planets.

In 1998, a team of astronomers led by Ron Gilliland of the Space
Telescope Science Institute embarked on the ambitious program of
searching for transits in some 40,000 stars in the core of the globular
cluster 47 Tucanae (Fig. 7). This
cluster is a particularly
interesting target for such a search for several reasons. (i) For
a typical star in the cluster, M* = 0.81,
R* = 0.92, and a typical "hot Jupiter"
orbital period (e.g., Porb = 3.8 days), the
probability of transit is 9.6% and the duration is 2.2 hours. For
a planet of radius Rp = 1.3 RJ
(where RJ is Jupiter's radius, as observed for the
transiting system HD 209458;
Charbonneau
et al. 2000,
Henry et al. 2000),
the expected transit depth is about 2%, easily detectable by
HST. (ii) Given that the frequency of "hot Jupiters" with orbital
periods shorter than 5 days (ten are known at the time of writing)
in the solar neighborhood is about 0.8%-1%, with a 10% chance of
transit one expects roughly one in every 1000 surveyed stars in
47 Tuc to show a transit (and therefore a few tens
of detections when monitoring
~ 40, 000 stars). (iii) The globular cluster 47 Tuc is about
11 billion years old and it has a total metallicity (abundance of
elements heavier than helium) of about one-third that of the Sun
(Salaris and Weiss 1998).
The frequency of planets in such an environment can therefore have
important implications for models of planet formation.

The Hubble Space Telescope observed 34,091 stars in 47 Tuc,
obtaining time series photometry over a period of 8.3 days
(continuously, except for Earth occultations and passages through the
South Atlantic Anomaly). A more detailed calculation of the expected
number of transits, taking into account the actual distribution of
V magnitudes of the stars in the sample
(Gilliland et
al. 2000)
and time series noise, showed that 17 transits should have been
seen, assuming the same frequency of hot Jupiters as in the solar
neighborhood. None was detected! Undoubtedly, this was not a problem
with the detection method. As many as 75 variable stars have
actually been detected. Furthermore, an eclipsing system with a period
of 1.34 days and an eclipse depth of ~ 3% was actually
discovered. However, the presence of a secondary eclipse in the system
showed that this was a grazing eclipse by a low-mass (K dwarf) star
and not a planet.

The direct implication is therefore that with a very high degree of
confidence the frequency of hot Jupiters in 47 Tuc is at most
1/10 that in the solar neighborhood.

The main question is then: why are there much fewer orbiting planets in
47 Tuc? There are, in principle, two possible
explanations for the paucity of planets in orbits around globular
cluster stars: (i) Planets do not form at all (or form much more rarely) in
globular clusters. (ii) Planets are torn from their parent stars.

Planet formation may be suppressed in old stellar clusters
because of two main reasons: low metallicity, or photoevaporation of
protoplanetary disks.

Conventional wisdom of giant planet formation suggests that this is a
two-step process. In the first, the collisional accumulation of rocky
and big planetesimals leads to a runaway growth of a solid core
(e.g., Lissauer
1987)
of about ten Earth masses (10
M). In the
second, the core acquires a gaseous atmosphere, which eventually
collapses, leading to the rapid accretion of hydrogen and helium from
the protoplanetary disk. One might suspect, therefore, that in
low-metallicity environments, the nucleation of dust grains would be
greatly suppressed, and concomitantly planets would form more
rarely. Furthermore, it has generally been noted that stars which bear
planets are, on average, enriched in metals in comparison to the Sun
(e.g.,
Gonzalez 1997,
Butler et
al. 2000,
Laughlin 2000,
Reid 2002),
and this trend is even more pronounced for the short-period
planets. Thus, the paucity of hot Jupiters in 47 Tuc may simply
reflect the cluster's low metallicity.

There is another reason why giant planet formation may be
suppressed in dense stellar clusters. The disk around any star in a
cluster is exposed to ultraviolet radiation from massive cluster
stars. This radiation heats the disk surface, raises the sound speed,
cs, and causes gas beyond a radius of

where is the flux of
ionizing photons and d is the disk's distance from the emitting
source. In a star forming region like Orion, the ionizing flux is of
order ~ 1049
s-1, of the same order as the flux expected in a cluster with
ncluster ~ 103 members. The mass loss rate
from one of the disks in Orion, HST 182-413, has been estimated from HST
observations to be
outflow ~ 4
× 10-7
M
yr-1. Since the mass of that disk is estimated to be
Johnstone et
al. 1998) Mdisk ~ 0.04
M, the disk
lifetime is expected to be
disk ~
Mdisk /
outflow ~
105 yr. For somewhat smaller disk sizes (e.g., like that
in the solar system ~ 30 AU) the disk lifetime can be somewhat
extended (the EUV-induced flow scales as
rdisk3/2). Nevertheless, the disk lifetime
may be significantly shorter than the planet formation timescale,
estimated to be of order 106-107 yrs (e.g.,
Shu et al. 1993,
Pollack et
al. 1996).
Armitage (2000)
calculated the expected disk lifetime as a function of
the cluster richness. He found that giant planet formation is strongly
suppressed in custers with ~ 105 stars out to around
1 pc or more.

There are two ways in which, in principle at least, the conclusion of a
low probability for planet formation in clusters, due to disk
destruction, may be avoided: (i) If giant planet formation occurs
not via a core accretion mechanism, but rather through direct and rapid
(within ~ 103 yr) fragmentation (due to a gravational
instability) into self-gravitating clumps of gas (e.g.,
Boss 2000,
Mayer et al. 2002).
(ii) If the formation of high-mass stars (which produce the
photoevaporating radiation) is significantly delayed (by ~
106 yr) compared to the formation of low mass stars. At
present both of these processes are sufficiently uncertain that no
definitive conclusion about their viability can be drawn.

The second possible explanation for the absence of "hot Jupiters" in
47 Tuc is that even if giant planets do form, they
are torn away
from their parent stars because of encounters in the crowded cluster
environment, and thus cannot exhibit transits. This possibility has been
investigated in some detail by
Davies and
Sigurdsson (2001).
The cross-section for two stars with a relative velocity at infinity
V to
pass within Rmin from each other is given by

(8)

where V is the relative velocity (V2
(M1 + M2) / Rmin)
at closest approach. The second term expresses the effect of
gravitational focusing. When V >>
V, as
is expected in globular clusters,
Rmin. The timescale for an encounter between a
star-planet system and a star is of order
(enc = 1/nV)

(9)

where n is the number density of stars of mass M and
d is the semimajor axis of the planetary orbit. Encounters
therefore occur on a timescale that is much shorter than a Hubble time
in a cluster like 47 Tuc, which has a density of about
1.5 × 105 pc-3 at its center and about
an order of magnitude lower at its half-mass radius (e.g.,
Howell et
al. 2000).
Generally, binaries (with masses
M1 and M2 for the primary and
secondary, respectively) in which the binding energy is lower than the
kinetic energy of the colliding star (of mass M3) are
disrupted. The condition for breakup is

(10)

Since M2 << M1,
M3, in the case of a star-planet system, breakup of
the system is expected to occur with a high probability when the third
star passes within a distance d.
Davies and
Sigurdsson (2001)
performed a large number of simulations for various values of
V /
Vorb and considered both encounters (of star-planet
systems) with single stars and with binaries.
They found that wide (d 0.3 AU)
planetary systems are likely to be broken up within the half-mass radius
of 47 Tuc, but tighter systems (d 0.1 AU) or
systems in less dense regions may survive. The results of Davies and
Sigurdsson still do not provide a complete explanation for the absence
of transits in 47 Tuc. Future observations, perhaps of less dense,
somewhat higher metallicity clusters (like NGC 6352) will be
required to explain which factor is responsible for the dearth of
planetary transits in 47 Tuc. An attempt to detect transits
associated with Galactic bulge and disk stars (that span 1.5 dex in
metallicity, and are in an environment that is orders of magnitude less
dense than the center of a globular cluster) would also be very
valuable. An understanding of the environments that are either conducive
to or prohibitive for the existence of planetary transits may constitute
an important step in the study of planet formation.